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Ring-theory
New post in Ring-theory
Show that $\Bbb R[x]/\langle x^{2}+1\rangle$ is a field.
August 18th, 2022
ring-theory
abstract-algebra
Is the set of all 2x2 matrices a ring with zero divisors?
August 15th, 2022
abstract-algebra
ring-theory
Structure theorem of Artinian rings
November 7th, 2022
commutative-algebra
ring-theory
Describe all extensions of the identity map of $\mathbb{Q}$ to an isomorphism mapping $\mathbb{Q}(\sqrt[3]{2},\sqrt{3})$
April 9th, 2020
abstract-algebra
ring-theory
finite-groups
group-theory
If R is an integral domain disprove the RxR is an integral domain?
December 19th, 2020
abstract-algebra
ring-theory
Let $M$ be a maximal ideal of a ring $R$. Is $M[x]$ a maximal ideal of $R[x]$?
August 1st, 2022
ring-theory
abstract-algebra
ideals
Gaussian integers modulo n. Multiplication table for $\mathbb Z_3[i]$.
August 1st, 2022
ring-theory
group-theory
abstract-algebra
Prove that R is a field ↔ The only ideals in R are R(0) and (0).
January 23rd, 2020
ring-theory
abstract-algebra
ideals
Finite integral domain
February 4th, 2020
ring-theory
abstract-algebra
integral-domain
finite-rings
finite-fields
Every maximal ideal is a prime ideal
September 7th, 2020
abstract-algebra
ring-theory
Show that $\mathbb{Z}_n$ is local ring iff $n$ is a power of a prime number
August 1st, 2022
ring-theory
The quotient ring $\mathbb{Z}[i]/(1 + i)$
June 5th, 2020
abstract-algebra
ring-theory
ideals
gaussian-integers
Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
August 1st, 2022
abstract-algebra
modules
field-theory
ring-theory
polynomials
Prove that if $R$ is a principal ideal ring and $S$ is a multiplicatively closed subset of $R$ then $S^{-1}R$ is also a principal ideal ring.
August 1st, 2022
commutative-algebra
ring-theory
Definition of residue in context of the polynomial ring of $\mathbb{Z}[x]/(f)$?
February 10th, 2022
ring-theory
polynomials
abstract-algebra
Understanding the quotient ring $\mathbb{Q}[x]/x^2$ up to isomorphism
August 1st, 2022
ring-theory
abstract-algebra
How to factor polynomials into irreducible factors in a particular ring?
August 1st, 2022
abstract-algebra
factoring
finite-fields
field-theory
ring-theory
Proving that End(V) is isomorphic to a matrix ring
August 1st, 2022
linear-algebra
ring-theory
abstract-algebra
Subfield of a field F
August 1st, 2022
ring-theory
field-theory
finite-fields
abstract-algebra
Ring of Fractions Isomorphic to Subring of Quotient Field.
July 18th, 2020
abstract-algebra
integration
ring-theory
Give an example to show that a factor ring of an integral domain may be a field
August 1st, 2022
ring-theory
abstract-algebra
How to check if a function is an homomorphism?
August 1st, 2022
ring-theory
modular-arithmetic
Prove a Field is a commutative ring with identity
August 1st, 2022
ring-theory
Find ring homorphisms from $\Bbb Z_2$ to $\Bbb Z_6$
August 1st, 2022
abstract-algebra
ring-theory
Solve the equation $3x=2$ in the fields $\mathbb Z_7$ and $\mathbb Z_{23}$
October 11th, 2020
ring-theory
Prove $R \times R$ is NOT an integral domain
August 1st, 2022
abstract-algebra
ring-theory
Finitely generated ring.
August 1st, 2022
ring-theory
finitely-generated
Noetherian group rings
August 1st, 2022
ring-theory
group-theory
noetherian
amenability
Left ideals of matrix rings are direct sum of column spaces?
November 18th, 2020
matrices
abstract-algebra
ring-theory
ideals
Matrix rings and ideals
November 25th, 2020
ideals
discrete-mathematics
ring-theory
abstract-algebra
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